# Quantum Spectral Reasoning: A Non-Neural Architecture for Interpretable Machine Learning

arXiv: https://arxiv.org/abs/2508.03170 · HTML: https://mlsanity.com/paper/2508.03170/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 9 of 9)

- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Towards AI-Complete Question Answering: A Set of Prerequisite Toy Tasks](https://mlsanity.com/paper/1502.05698/) (2015)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence](https://mlsanity.com/paper/2002.06177/) (2020)
- [CLUTRR: A Diagnostic Benchmark for Inductive Reasoning from Text](https://mlsanity.com/paper/1908.06177/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)

## Abstract (arXiv)

We propose a novel machine learning architecture that departs from conventional neural network paradigms by leveraging quantum spectral methods, specifically Pade approximants and the Lanczos algorithm, for interpretable signal analysis and symbolic reasoning. The core innovation of our approach lies in its ability to transform raw time-domain signals into sparse, physically meaningful spectral representations without the use of backpropagation, high-dimensional embeddings, or data-intensive black-box models. Through rational spectral approximation, the system extracts resonant structures that are then mapped into symbolic predicates via a kernel projection function, enabling logical inference through a rule-based reasoning engine. This architecture bridges mathematical physics, sparse approximation theory, and symbolic artificial intelligence, offering a transparent and physically grounded alternative to deep learning models. We develop the full mathematical formalism underlying each stage of the pipeline, provide a modular algorithmic implementation, and demonstrate the system's effectiveness through comparative evaluations on time-series anomaly detection, symbolic classification, and hybrid reasoning tasks. Our results show that this spectral-symbolic architecture achieves competitive accuracy while maintaining interpretability and data efficiency, suggesting a promising new direction for physically-informed, reasoning-capable machine learning.